In this study, we propose a new immersed boundary method for compressible fluid-structure interaction simulations. We take a partitioned coupling strategy that comprises three parts: fluid solver, structure solver, and fluid-structure boundary treatment. The fluid solver is implemented by a second-order finite volume scheme, and the structure is solved by an implicit finite element solver. For the boundary treatment, this method employs a multilevel marking algorithm to determine the direction from the inside of the structure to the outside. Following the direction, fluids that permeate the structure are transported out of the structure boundaries to satisfy the boundary conditions. This method strictly maintains mass conservation and uses no cross-boundary fitting or interpolation; thus, it appears to be convenient when treating complex-shaped or deformable structures and diminishes the singularity problem. The 1D and 2D numerical experiments show that our method is capable of obtaining approximately first-order convergent results, agreeing well with the published data. The method's limitations are discussed in the conclusion.

在这项研究中，我们提出了一种用于可压缩流体-结构相互作用模拟的新的浸入边界方法。我们采用一种分区耦合策略，该策略包括三个部分：流体求解器，结构求解器和流固边界处理。流体求解器通过二阶有限体积方案实现，结构通过隐式有限元求解器求解。对于边界处理，此方法采用多级标记算法来确定从结构内部到外部的方向。沿着该方向，渗透到结构中的流体被运出结构边界，以满足边界条件。该方法严格保持质量守恒，并且不使用跨边界拟合或内插；从而，当处理复杂形状或可变形的结构时，它似乎很方便，并且减少了奇点问题。一维和二维数值实验表明，我们的方法能够获得近似一阶收敛的结果，与已发表的数据非常吻合。结论中讨论了该方法的局限性。